You still need to share this with AA. Something went seriously awry here. The only possible thing that I can think of is somehow or another, your electronic ticket got reset from checked in to not checked in for your connection to SNA while you were traveling to ORD. It sounds like the gate was a zoo, so there could've been some strange stuff going on with the flight.
I'd write AA a letter, tell them that you did accept the vouchers (I'm assuming you got $300 for each of you, so $600 total?), but you are still displeased with the way the entire situation was handled. You should describe the entire process about checking in in LHR and receiving your boarding cards all the way to SNA, and then presenting yourselves for boarding only to be rejected by the gate reader. I've got a sneakin' suspicion that something happened to reset your e tickets to show not checked in, and that is something that Customer Relations can determine by reviewing the history of your PNR.